The generator matrix

 1  0  0  0  1  1  1 3X+2  1 3X+2  1  X  1 2X+2  1 3X+2 3X  1  1  1 X+2 3X  0  2 3X  1  1  1  1  1 2X  1  1 3X+2  X  1  1  1  2 3X  1  0 2X+2 3X  1  1  1 X+2 3X+2  1 2X  1 3X+2  1  0 2X+2  X  1  1  2  1 3X+2  1  0  1  0 2X+2  1  1  1  X  1  2  1  1  X  X  1  0  1  X  1  1  1 2X X+2 3X+2 2X 2X  1
 0  1  0  0 2X  3 3X+1  1 2X+2 2X+2 2X+2  1 3X+3  1  1 2X+2  0 3X+3 2X+1 X+1  1 3X  1  1  1  X  2 X+3  0 X+2  1  X 2X+2 3X+2 X+2  X 3X+1 X+3  1 3X+2 3X+2  1  1  1  3 2X+1 3X+3 2X  1 2X  1  X  1 X+2 2X  1  1 X+1 3X+1 3X X+2  0  2  1  3 2X+2  1  X 3X+2 3X+1  2  1 X+2 3X+3 X+1  1  1  2  1 X+2  0 2X+2 2X 3X+2 3X 2X  1  1  1  1
 0  0  1  0  2 2X 2X+2 2X+2  1  1 X+3 X+3  3 X+1 3X+1  2  1 2X+2 2X X+3 2X+1  1 X+1  0 2X 2X+1 2X+1 3X+1  X X+2 3X+2 3X 3X  1 X+2 3X+3 3X+1 X+2 X+2  1  3 2X 2X+1 X+3 X+3  3 X+2  1 3X+1  0 3X+2 X+3  3 2X  1 2X 3X+2 3X+2 2X+3  1 3X  X X+3 3X+3  2  X  3  3  2 2X+3 3X  1  1  2  3 3X+1 2X 3X+1 X+3 2X+3 3X  0 2X 2X+2 2X  1 3X+2 X+2  2  1
 0  0  0  1 3X+3 X+3 2X X+1 3X+1 X+3  0 2X+1 3X+2 3X 2X+1  1 2X+1  X  3 3X 3X  0 3X+1 2X+1 2X 3X 2X+1  1 2X+3 2X+2 2X+3 X+2 3X+3  1  1  2 3X+1 3X+3 2X 3X X+3 X+3  2 X+1 3X+2 X+2  2 3X+2 3X 2X+1 X+3  3  2 X+2 X+1 3X+2 X+1 X+2 2X+1 X+3 2X+1  1 X+2 2X+2  0  1  3  1  2 X+3  1  2 2X+1 X+1 2X 3X+1  3 X+2  3 3X+1  1 X+2 3X+3 2X+1  1  0  0 3X  3 X+1

generates a code of length 90 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+604x^83+1928x^84+3326x^85+4730x^86+5794x^87+6590x^88+6746x^89+7337x^90+6738x^91+6341x^92+5374x^93+3869x^94+2622x^95+1783x^96+922x^97+455x^98+178x^99+81x^100+44x^101+33x^102+32x^103+4x^104+4x^105

The gray image is a code over GF(2) with n=720, k=16 and d=332.
This code was found by Heurico 1.16 in 55 seconds.